“I wouldn’t mind a cuppa” does not merely say that you have no objection to a drink. It is a gentle way of saying, “Yes, I’d quite like one.” Wouldn’t mind softens the wish: the speaker is willing to accept and usually does want the offer. Cuppa is informal and traditionally means a cup of tea; in everyday Australian use, it may also cover tea or coffee.
A: Tea?
B: I wouldn’t mind a cuppa, thanks.
It is softer than I want tea, but less uncertain than maybe. If you do not want a drink, say No thanks. When you answer an offer with I wouldn’t mind, the other person will normally hear a positive response. The important point is not the word-for-word negative form, but the positive wish it politely contains.
https://dictionary.cambridge.org/dictionary/english/mind
https://www.collinsdictionary.com/dictionary/english/cuppa
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